Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int i, z = 0, p, l, j;
  cin >> p;
  vector<int> v;
  for (i = 1; z < p; i++) {
    z = z + i;
    v.push_back(z);
  }
  for (j = 0; j < v.size(); j++) {
    l = p - v[j];
    vector<int>::iterator o;
    o = find(v.begin(), v.end(), l);
    if (o != v.end()) {
      cout << "YES";
      return 0;
    }
  }
  if (j == v.size()) {
    cout << "NO";
  }
}